Question

PreLab Questions:
1. What is the definition of moment of inertia I? (Write down a
general equation for I and explain what the symbols in the equation
mean.) What are the units of I in the cgs system(cgs =
centimeter-gram-second)? What are the units of I in the MKS system?
(MKS = meter-kilogram-second, also called the SI system.)
2. Use the definition of I to show that the moment of inertia of a
thin hoop of mass M, radius R, and negligible thickness is given by
Ihoop = MR2 .
3. Use the definition of moment of inertia to show that Idisk = 21
MR2 . [Hint: Use the integralformofeq�n(11), I=?? r2 dV,where ?=M/V
isthedensityofthedisk.]
4. A solid disk of radius R and mass M is glued to a thin hoop of
radius R and mass m (m?M). The symmetry axes of the disk and hoop
are aligned. What is Itotal , the total moment of inertia of the
disk + hoop about the axis of symmetry?
5. The disk has a little hub at its center (in the shape of an
annulus) with a mass m = 70�1 grams and with inner and outer radii
of r1 = 6.4 mm and r2 = 16.8 mm. Use eq�n (13) to compute the
moment of inertia of the hub. (Careful of your units! Are you going
to use kilograms or grams?, meters or centimeters or ...?)
6. What are the units of the torsion constant ? in the MKS system?
In the cgs system?
7. What is the definition of torque? (Don�t just give a vague,
qualitative definition; give the precise, technical definition, as
given in physics text books. As usual, if you give an equation,
explain what the terms in the equation mean.) What are the units of
torque in the MKS system?
8. Consider a torsion pendulum consisting of a solid disk of mass M
and radius R, suspended from a wire with torsion constant ? Write
an equation which shows how the period T depends on M, R, and ?
What happens to the period T, if ?m, the amplitude of the angular
motion, is decreased by a factor of two?
9. Consider two disks, labeled A and B, with disk A having two
times the mass and three times the radius of disk B (MA = 2MB , RA
= 3RB). Each disk is suspended from a wire with same torsion
constant ?, and the period of each (TA, TB) is measured. What is
the
ratio TA TB ?
10. Consider a set of rods all of the same material and the same
length, but with differing radii, r. Assuming that you have the
correct value of the exponent n, show with a sketch what a graph of
? vs. rn should look like.